Factoring and Fourier Transformation with a Mach-Zehnder Interferometer

The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.Comment: 5 pages, 2 postscript figures; to appear in Phys.Rev.A, Nov. 1997; Figures contained only in replaced versio

Strict detector-efficiency bounds for n-site Clauser-Horne inequalities

An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented, for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the efficiency is greater than n/(2n-1). Thus, for a two-site two-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than 2/3. Secondly, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds 1/2.Comment: revtex, 5 pages, 1 figure (typesetting changes only

Bell's Theorem and Nonlinear Systems

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-Podolsky-Rosen-type experiments can be reproduced within deterministic models that include arbitrarily weak non-local effects.Comment: Accepted for publication in Europhysics Letters. 14 pages, no figures. In the Appendix (not included in the EPL version) the author says what he really thinks about the subjec

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure

Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical expression of bound of Bell operator for any given pure state. Our result not only manifest some properties of Bell inequality, for example which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also give the explicit values of maximal violation for any pure state. Finally we point out that for two qubits systems there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

Does Clauser-Horne-Shimony-Holt Correlation or Freedman-Clauser Correlation lead to the largest violation of Bell's Inequality?

An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment which can actually be performed with present technology to test local realism. Quantum mechanics violate this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities (for example, Clauser-Horne-Shimony-Holt inequality of 1969, Freedman-Clauser inequality of 1972, Clauser-Horne inequality of 1974) by a factor of $\sqrt 2$. Thus the magnitude of violation of the inequality derived in this paper is approximately $20.7$ larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.Comment: 15 pages, LaTeX file, no figure

Entropy inequalities and Bell inequalities for two-qubit systems

Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities in a mixed state of a two-qubit system are: 1) The linear entropy of the state is not smaller than 0.5, 2) The sum of the conditional linear entropies is non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum of the conditional von Neumann entropies is not smaller than 0.280.Comment: Errors corrected. See L. Jakobcyk, quant-ph/040908

General criterion for the entanglement of two indistinguishable particles

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004

Atomic vapor-based high efficiency optical detectors with photon number resolution

We propose a novel approach to the important fundamental problem of detecting weak optical fields at the few photon level. The ability to detect with high efficiency (>99%), and to distinguish the number of photons in a given time interval is a very challenging technical problem with enormous potential pay-offs in quantum communications and information processing. Our proposal diverges from standard solid-state photo-detector technology by employing an atomic vapor as the active medium, prepared in a specific quantum state using laser radiation. The absorption of a photon will be aided by a dressing laser, and the presence or absence of an excited atom will be detected using the ``cycling transition'' approach perfected for ion traps. By first incorporating an appropriate upconversion scheme, our method can be applied to a wide variety of optical wavelengths.Comment: 4 pages, 2 figure

Substituting Quantum Entanglement for Communication

We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data is distributed among remote parties. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglement cannot be used to simulate communication among remote parties.Comment: 4 pages REVTeX, no figures. Minor correction